In an earlier work, we proposed a generalization for the Apollonian packing in arbitrary dimensions and showed that the resulting object in four, five, and six dimensions have properties consistent with the Apollonian circle and sphere packings in two and three dimensions. In this work, we investigate the generalization in seven and eight dimensions and show that they too have many of the properties of those in lower dimensions. In particular, the hyperspheres are tangent or do not intersect; they fill the hyperspace; the object includes a maximal cluster of mutually tangent hyperspheres; and there exists a perspective where all hyperspheres in the object have integer curvatures.

在较早的工作中，我们提出了对任意维度的Apollonian填充的概括，并显示了在四，五和六维中生成的对象具有与二维和三维中的Apollonian圆和球形填充物一致的属性。在这项工作中，我们研究了七个维度和八个维度的概括，并表明它们也具有较低维度的概括性。特别是，超球面是切线的或不相交的。它们填充了超空间；物体包括相互切线的超球面的最大簇；并且存在一个透视图，其中物体中的所有超球面都具有整数曲率。